Fixed-time adaptive hydraulic robotic arm force / position control method

Abstract

This invention discloses a fixed-time adaptive force / position control method for a hydraulic robotic arm. Addressing the problems of unmeasurable system velocity, model uncertainty, and the impact of external disturbances on control accuracy, this invention innovatively proposes a fixed-time differential-sliding mode observer. The unmeasurable velocity is estimated using a fixed-time differentiator, and the disturbance force is simultaneously estimated using a fixed-time sliding mode observer, overcoming the limitations of complex parameter tuning in traditional fixed-time extended state observers. Based on this, a command filtering and adaptive mechanism are integrated into the backstepping framework to construct a fixed-time command filtering adaptive force / position controller based on this observer. This method incorporates fixed-time stability theory into state observation and control law design, making the upper bound of the system convergence time independent of the initial state. This enables high-precision trajectory and force tracking control within a fixed time frame and effectively improves the system's robustness and control performance under unknown disturbances.

Description

Technical Field

[0001] This invention relates to a fixed-time adaptive force / position control method for hydraulic robotic arms, used for the control of multi-axis hydraulic systems such as hydraulic robotic arms and hydraulic outriggers, and belongs to the field of nonlinear control technology. Background Technology

[0002] High-precision trajectory tracking control of hydraulic robotic arms / outriggers faces multiple challenges, including strong nonlinearity, strong coupling, system uncertainties (such as internal leakage, dead zone, and changes in the bulk modulus of hydraulic fluid), and external disturbances. Dynamic surface backstepping, a widely used method in nonlinear electro-hydraulic system control, can effectively handle matched and unmatched disturbances. However, traditional dynamic surface backstepping introduces filtering errors and cannot guarantee convergence within a set time. In applications requiring high response speed, such as wheel-leg-arm hybrid obstacle crossing, failure of force / position control to converge within a fixed time may lead to system instability.

[0003] Due to space and cost constraints, hydraulic robotic arms are typically equipped only with cylinder displacement and pressure sensors, making it impossible to directly measure the end effector force and cylinder speed. Therefore, methods such as Kalman filtering and disturbance observers are often used for state reconstruction. However, the convergence time of these methods cannot be strictly set, and their performance is affected by the initial values. Furthermore, although observers with fixed-time convergence properties (such as fixed-time extended state observers) have been proposed, their parameter tuning is complex and they are not suitable for hydraulic equipment with large load disturbances. Summary of the Invention

[0004] The purpose of this invention is to provide a fixed-time adaptive hydraulic robotic arm force / position control method, which can complete speed and external force estimation and position / force tracking control within a preset fixed time.

[0005] A fixed-time adaptive force / position control method for a hydraulic robotic arm, characterized by comprising the following steps: S1. Fixed-time observation of state and disturbance: Construct a fixed-time differential-sliding mode observer, which integrates a fixed-time differentiator and a sliding mode disturbance observer, for fixed-time estimation of joint angular velocities that cannot be directly measured in the hydraulic manipulator system, as well as external disturbance forces mapped to the joint space. S2. Controller Design: Based on the backstepping method framework, fixed-time command filtering adaptive controllers for the position tracking control loop and the force tracking control loop are designed respectively; the controllers use the joint angular velocity and disturbance estimate obtained from the aforementioned steps, as well as the system state feedback, as inputs; S3. Control Execution and Output: Set the position control or force control mode according to the task; input the expected command of the current mode, the actual state of the system, and the speed and disturbance force estimates obtained from step S1 into the designed fixed-time command filter adaptive controller; the controller calculates and generates the proportional valve control current in real time, drives the hydraulic robotic arm to perform actions, and realizes fixed-time stable tracking control of the target trajectory or target force.

[0006] To achieve rapid estimation of joint angular velocities and external forces in a hydraulic robotic arm system that cannot be directly measured, this invention designs a fixed-time differential-sliding mode observer in step S1. Its specific design and construction are as follows: 1. Establishment of system dynamics model The observer design is based on modeling the hydraulic manipulator system. Considering both the dynamic characteristics of the manipulator links and the dynamic characteristics of the hydraulic drive system, the following third-order nonlinear state-space model is established: (1) in, These are the joint angle, angular velocity, and joint cylinder force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... This represents the lumped disturbance consisting of joint external forces and unmodeled errors. This indicates an error due to the hydraulic system not being modeled. , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, diagonal matrix and This indicates a quantity related to the effective area and volume of the hydraulic cylinder. , This represents quantities related to the hydraulic bulk modulus and valve flow coefficient.

[0007] 2. Design of Fixed-Time Differential-Sliding Mode Observer The dynamic equation of the fixed-time differential-sliding mode observer is: (2) in, These are the estimated values ​​of joint angle, angular velocity, and angular acceleration, respectively. , , It is a sufficiently small positive number and satisfies the cyclic relationship. , Observation gain Make For the Hurwitz matrix: (3) It's virtual speed. It is an auxiliary variable for perturbation estimation, and the estimated value of the perturbation. , ; It is the defined sliding surface. , It is a positive gain coefficient. , These are the coefficients of the power term used for fixed-time convergence. , It is a disturbance The upper realm, .

[0008] It can be proven using Lyapunov stability theory that the errors in velocity estimation and external force estimation will converge to a small neighborhood of the origin within a fixed time, and the upper bound of the convergence time depends only on the design parameters and is independent of the initial state of the system.

[0009] The fixed-time differential-sliding mode observer method described above is also applicable to internal disturbances in hydraulic systems. The estimate.

[0010] 3. Design of an Adaptive Controller Based on a Fixed-Time Differential-Sliding Mode Observer To achieve high-precision trajectory and force tracking of the hydraulic robotic arm under time-varying hydraulic parameters and external disturbances, this invention designs a fixed-time command filtering adaptive backstepping controller in step S2. This controller integrates command filtering and adaptive mechanisms synchronously within the fixed-time backstepping framework, which are described in detail below for the position control loop and force control loop.

[0011] a) Position control loop design The goal of the position control loop is to drive the joint angles of the robotic arm. Precisely track the desired trajectory .

[0012] First, define the state tracking errors of the system at each order: (4) in, These are the state errors of joint angle, joint speed, and hydraulic cylinder output force, respectively. It is the expected joint trajectory. These are the virtual control laws of the filter output; The filter is designed as a first-order low-pass filter: (5) in, , It is a time constant. , It is the virtual input of the filter.

[0013] To eliminate the filtering error introduced by the filter, a tracking error compensation mechanism is introduced. The tracking error compensation is defined as follows. for: (6) Filtering compensation signal The dynamic equation is: (7) in, , , is a positive definite diagonal matrix ; Based on the backstepping framework, virtual control laws are designed step by step, starting from the first subsystem. A fixed-time convergence term is introduced in each step, and an adaptive mechanism is introduced for the time-varying order of parameters.

[0014] First-order compensation tracking error The derivative is: (8) Selection of Lyapunov function for first-order error Its derivative is: (9) First-order virtual control law Designed as follows: (10) Second-order compensation tracking error The dynamic equation is expressed as: (11) definition Lyapunov function selection for second-order error Its derivative is: (12) The second-order virtual control law is designed as follows: (13) Third-order compensation tracking error The dynamic equation is expressed as: (14) Due to parameters It is time-varying, and an adaptive rate is designed to compensate for parameter errors. For an n-dimensional vector... Projection mapping Represented as: (15) The adaptive rate is designed as follows: (16) It satisfies the following properties: (17) in It is a positive definite diagonal gain matrix. It is an adaptive function; used to estimate the diagonal matrix. The parameters are defined. , , , Adaptive rate , , , .

[0015] Choice of Lyapunov function for third-order error: (18) The derivative is: (19) Final input Designed as follows: (20) b) Force control loop design When the robotic arm requires precise contact force control, it switches to force control mode. The goal of the force control loop is to ensure that the actual contact force... Tracking Expectancy .

[0016] Define tracking error The derivative of the desired force is obtained through a first-order filter: (twenty one) Force control loop input Designed as follows: (twenty two) Step S3 is responsible for the online operation of the entire control algorithm, and its workflow is as follows: Select the position or force control mode according to the task instructions.

[0017] Joint angle measured by sensor Hydraulic cylinder force and the velocity estimation of the real-time output of the differential-sliding mode observer. External force estimation The data is input into the controller.

[0018] The controller receives the desired trajectory based on the selected mode. or expectation and output proportional valve control current. This drives the robotic arm to move.

[0019] The sensor continuously detects new states, forming a closed-loop control to achieve stable tracking of trajectory or force over a fixed period of time.

[0020] Compared with the prior art, the present invention has the following beneficial effects: (1) To address the control challenges posed by the lack of a fixed-time disturbance observation method that does not rely on velocity measurement when hydraulic robotic arms face large load disturbances, a fixed-time differential-sliding mode observer method is proposed. This method can estimate joint velocity and external force disturbance within a pre-set time, and its convergence process does not depend on the initial state of the system.

[0021] (2) A force / position composite control method integrating fixed-time convergence, command filtering, and adaptive mechanism is proposed. Together, it solves the control problems caused by filtering errors, parameter uncertainties, and unknown disturbances in hydraulic multi-degree-of-freedom systems, ensuring that the system can track the desired trajectory and contact force within a fixed time independent of the initial state. Attached Figure Description

[0022] Figure 1 This invention relates to a hydraulic robotic arm force / position control method based on fixed-time adaptive control. Figure 2 This is a schematic diagram of a hydraulic robotic arm force / position control method based on fixed-time adaptive control according to the present invention. Figure 3 This is a tracking curve of the swing joint angle in an embodiment of the present invention; Figure 4 This is a pitch joint force tracking curve diagram in an embodiment of the present invention; Figure 5 This is a diagram of the angular velocity of the swing joint in an embodiment of the present invention; Figure 6 This is a diagram showing the external force disturbance of the pitch joint in an embodiment of the present invention; Detailed Implementation

[0023] The purpose of this invention is to provide a fixed-time adaptive hydraulic robotic arm force / position control method, which can complete speed and external force estimation and position tracking control within a pre-set fixed time, and its convergence performance does not depend on the initial state of the system.

[0024] To achieve the above-mentioned invention, the technical solution adopted by this invention is: a hydraulic robotic arm force / position control method based on fixed-time adaptive control, comprising the following steps: S1. Fixed-time observation of state and disturbance: Construct a fixed-time differential-sliding mode observer, which integrates a fixed-time differentiator and a sliding mode disturbance observer, for fixed-time estimation of joint angular velocities that cannot be directly measured in the hydraulic manipulator system, as well as external disturbance forces mapped to the joint space. S2. Controller Design: Based on the backstepping method framework, fixed-time command filtering adaptive controllers for the position tracking control loop and the force tracking control loop are designed respectively; the controllers use the joint angular velocity and disturbance estimate obtained from the aforementioned steps, as well as the system state feedback, as inputs; S3. Control Execution and Output: Set the position control or force control mode according to the task; input the expected command of the current mode, the actual state of the system, and the speed and disturbance force estimates obtained from step S1 into the designed fixed-time command filter adaptive controller; the controller calculates and generates the proportional valve control current in real time, drives the hydraulic robotic arm to perform actions, and realizes fixed-time stable tracking control of the target trajectory or target force.

[0025] To achieve accurate estimation of joint angular velocities and external forces in a hydraulic robotic arm system that cannot be directly measured, this invention designs a fixed-time differential-observer in step S1, the specific design and construction of which are as follows: 1. Establishment of system dynamics model The observer design is based on a precise model of the hydraulic manipulator system. Taking into account both the dynamic characteristics of the manipulator links and the dynamic characteristics of the hydraulic drive system, the following third-order integrated nonlinear state-space model is established: (1) in, These are the joint angle, angular velocity, and joint cylinder force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... This represents the lumped disturbance consisting of joint external forces and unmodeled errors. This indicates an error due to the hydraulic system not being modeled. , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, diagonal matrix and This indicates a quantity related to the effective area and volume of the hydraulic cylinder. , This represents quantities related to the hydraulic bulk modulus and valve flow coefficient. 2. Design of Fixed-Time Differential-Sliding Mode Observer The dynamic equation of the fixed-time differential-sliding mode observer is: (2) in, These are the estimated values ​​of joint angle, angular velocity, and angular acceleration, respectively. , , It is a sufficiently small positive number and satisfies the cyclic relationship. , Observation gain Make For the Hurwitz matrix: (3) It's virtual speed. It is an auxiliary variable for perturbation estimation, and the estimated value of the perturbation. , ; It is the defined sliding surface. , It is a positive gain coefficient. , These are the coefficients of the power term used for fixed-time convergence. , It is a disturbance The upper realm, .

[0026] It can be proven using Lyapunov stability theory that the errors in velocity estimation and external force estimation will converge to a small neighborhood of the origin within a fixed time, and the upper bound of the convergence time depends only on the design parameters and is independent of the initial state of the system.

[0027] The fixed-time differential-sliding mode observer method described above is also applicable to internal disturbances in hydraulic systems. The estimate.

[0028] 3. Design of a Fixed-Time Command Filtering Adaptive Force / Bit Controller To achieve high-precision trajectory and force tracking of the hydraulic robotic arm under model uncertainties and external disturbances, this invention designs a fixed-time command filtering adaptive backstepping controller in step S2. This controller integrates command filtering and adaptive mechanisms simultaneously within the fixed-time backstepping framework, which are described in detail below for the position control loop and force control loop.

[0029] a) Position control loop design The goal of the position control loop is to drive the joint angles of the robotic arm. Precisely track the desired trajectory .

[0030] First, define the state tracking errors of the system at each order: (4) in, These are the state errors of joint angle, joint speed, and hydraulic cylinder output force, respectively. It is the expected joint trajectory. These are the virtual control laws of the filter output; The filter is designed as a first-order low-pass filter: (5) in, , It is a time constant. , It is the virtual input of the filter; To eliminate the filtering error introduced by the filter, a tracking error compensation mechanism is introduced. The tracking error compensation is defined as follows. for: (6) Filtering compensation signal The dynamic equation is: (7) in, , , is a positive definite diagonal matrix ; Based on the backstepping framework, virtual control laws are designed step by step, starting from the first subsystem. A fixed-time convergence term is introduced in each step, and an adaptive mechanism is introduced for the time-varying order of parameters.

[0031] First-order compensation tracking error The derivative is: (8) Selection of Lyapunov function for first-order error Its derivative is: (9) First-order virtual control law Designed as follows: (10) Second-order compensation tracking error The dynamic equation is expressed as: (11) definition Lyapunov function selection for second-order error Its derivative is: (12) The second-order virtual control law is designed as follows: (13) Third-order compensation tracking error The dynamic equation is expressed as: (14) Due to parameters It is time-varying, and an adaptive rate is designed to compensate for parameter errors. For an n-dimensional vector... Projection mapping Represented as: (15) The adaptive rate is designed as follows: (16) It satisfies the following properties: (17) in It is a positive definite diagonal gain matrix. It is an adaptive function; used to estimate the diagonal matrix. The parameters are defined. , , , Adaptive rate , , , .

[0032] Choice of Lyapunov function for third-order error: (18) The derivative is: (19) Final input Designed as follows: (20) b) Force control loop design When the robotic arm requires precise contact force control, it switches to force control mode. The goal of the force control loop is to ensure that the actual contact force... Tracking Expectancy

[0033] Define tracking error The derivative of the desired force is obtained through a first-order filter: (twenty one) Force control loop input Designed as follows: (twenty two) Step S3 is responsible for the online execution of the entire control algorithm. Its workflow is as follows: The control mode selects either position control or force control based on high-level task instructions. In operations requiring alternating use of the two modes (such as auxiliary support for a robotic arm), the mode switching is triggered based on the real-time estimate of external disturbances by a disturbance observer. When this value exceeds a preset threshold, the control mode switching is triggered.

[0034] Joint angle measured by sensor Hydraulic cylinder force and the velocity estimation output by the observer in real time External force estimation The data is input into the controller.

[0035] The controller receives the desired trajectory based on the selected mode. or expectation and output proportional valve control current. This drives the robotic arm to move.

[0036] The sensor continuously detects new states, forming a closed-loop control to achieve stable tracking of trajectory or force over a fixed period of time.

[0037] To verify the effectiveness of the control method of this invention, a simulation analysis of a two-degree-of-freedom hydraulic manipulator was conducted in the Matlab environment. During the simulation, the swing joint of the hydraulic manipulator performed trajectory tracking, and the pitch joint performed force tracking. The system was not equipped with joint velocity sensors or external force sensors. The parameter design is as follows: Table 1 Parameter Table

[0038] It is the gain coefficient of the force control loop. These are the hydraulic coefficients for positive and negative currents, respectively.

[0039] The trajectory tracking simulation results of the two-degree-of-freedom hydraulic manipulator are as follows: Figure 3 As shown, simulation results demonstrate that the proposed adaptive command filtering method based on a fixed-time differential-sliding mode observer can achieve time-based tracking of the desired trajectory.

[0040] The force tracking simulation results of the two-degree-of-freedom hydraulic manipulator are as follows: Figure 4 As shown, simulation results indicate that the force tracking error of the proposed command filtering adaptive method based on a fixed-time differential-sliding mode observer converges within a fixed time.

[0041] The joint angular velocity estimation results are as follows Figure 5 As shown in the figure, the results demonstrate that the proposed fixed-time differential-sliding mode observer can achieve effective joint velocity estimation within a fixed time.

[0042] Simulation results of joint perturbation estimation are as follows Figure 6 As shown, the results demonstrate that the proposed fixed-time differential-sliding mode observer can achieve fixed-time estimation of the disturbance force.

Claims

1. A method for force / position control of a hydraulic robotic arm based on fixed-time adaptive control, characterized in that, Includes the following steps: S1. Fixed-time observation of state and disturbance: Construct a fixed-time differential-sliding mode observer, which integrates a fixed-time differentiator and a sliding mode disturbance observer, for fixed-time estimation of joint angular velocities that cannot be directly measured in the hydraulic manipulator system, as well as external disturbance forces mapped to the joint space. S2. Controller Design: Based on the backstepping framework, fixed-time command filtering adaptive controllers for the position tracking control loop and the force tracking control loop are designed respectively. The controller takes the joint angular velocity and disturbance estimate obtained from the aforementioned steps, as well as the system state feedback, as inputs. S3. Control Execution and Output: Set the position control or force control mode according to the task; input the expected command of the current mode, the actual state of the system, and the speed and disturbance force estimates obtained from step S1 into the designed fixed-time command filter adaptive controller; the controller calculates and generates the proportional valve control current in real time, drives the hydraulic robotic arm to perform actions, and realizes fixed-time stable tracking control of the target trajectory or target force.

2. The hydraulic robotic arm force / position control method based on fixed-time adaptive control according to claim 1, characterized in that: The fixed-time differential-sliding mode observer in step S1 is constructed based on the following hydraulic manipulator dynamics model: (1) in, These are the joint angle, angular velocity, and joint cylinder force, respectively. Represents the inertial force matrix. Represents the vectors of the Coriolis force and the centrifugal force. Represents the gravity vector. Let the joint friction force vector be... This represents the lumped disturbance consisting of joint external forces and unmodeled errors. This indicates an error due to the hydraulic system not being modeled. , representing the velocity Jacobian matrix between the cylinder and the joint. , representing the Jacobian matrix between cylinder force and joint torque, diagonal matrix and This indicates a quantity related to the effective area and volume of the hydraulic cylinder. , This represents quantities related to the hydraulic bulk modulus and valve flow coefficient. The dynamic equation of the fixed-time differential-sliding mode observer is: (2) in, These are the estimated values ​​of joint angle, angular velocity, and angular acceleration, respectively. , , It is a sufficiently small positive number and satisfies the cyclic relationship. , Observation gain Make For the Hurwitz matrix: (3) It's virtual speed. It is an auxiliary variable for perturbation estimation, and the estimated value of the perturbation. , ; It is the defined sliding surface. , It is a positive gain coefficient. , These are the coefficients of the power term used for fixed-time convergence. , It is a disturbance The upper realm, .

3. The hydraulic robotic arm force / position control method based on fixed-time adaptive control according to claim 1, characterized in that, The fixed-time command filtering adaptive controller in step S2 has its position control loop designed as follows: Define state error: (4) in, These are the state errors of joint angle, joint speed, and hydraulic cylinder output force, respectively. It is the expected joint trajectory. These are the virtual control laws of the filter output; Design a filter: (5) in, , It is a time constant. , It is the virtual input of the filter; Define compensation tracking error for: (6) Filtering compensation signal The dynamic equation is: (7) in, , , is a positive definite diagonal matrix ; First-order virtual control law Designed as follows: (8) Second-order virtual control law Designed as follows: (9) in , ; Due to parameters It is time-varying, and an adaptive rate is designed to compensate for parameter errors for an n-dimensional vector. Projection mapping Represented as: (10) The adaptive rate is designed as follows: (11) It satisfies the following properties: (12) in It is a positive definite diagonal gain matrix. It is an adaptive function; used to estimate the diagonal matrix. The parameters are defined. , , , Adaptive rate , , , ; enter Designed as follows: (13) The fixed-time command filter adaptive controller in step S2 has its force control loop designed as follows: Define force tracking error: (14) in, The desired cylinder force is to be tracked; the derivative of the desired force is obtained through a first-order filter: (15) Force control loop input Designed as follows: (16)。 4. The hydraulic robotic arm force / position control method based on fixed-time adaptive control according to claim 1, characterized in that, In step S3: a) Select either position control mode or force control mode according to the requirements of the task; b) Input the desired command corresponding to the selected mode, the system state feedback, and the speed and disturbance estimation state observed in step S1 into the fixed-time command filter adaptive force / position controller designed in step S2. c) The controller calculates and outputs the control current of the proportional valve in real time based on the input signal, drives the hydraulic robotic arm to move, and achieves fixed-time stable tracking of trajectory or force.

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